Telegram clients are open source. I downloaded and built MacOS version recently - it was very straightforward.

https://telegram.org/apps#source-code

Encryption for secret chats doesn't involve server, so technically it can be analyzed.

It's a pity Telegram decided to roll their own encryption scheme. I use Telegram a lot for daily business because it's superior desktop messenger product. I would gladly participate if somebody started a crowd-funding for Telegram's security and encryption audit.